To compute \(T(X_1^n)\) , we use an iterative re-weighting algorithm. This algorithm is rather well known to compute M-estimators, see [1]} and it has already been extensively studied. The principle is to rewrite the definition of \(T(X_1^n)\)  from equation (REF ) as
\(T(X_1^n)\sum _{i=1}^n\frac{\psi \left(\Vert X_i-T(X_1^n)\Vert \right)}{\Vert X_i-T(X_1^n)\Vert }=\sum _{i=1}^nX_i\frac{\psi \left(\Vert X_i-T(X_1^n)\Vert \right)}{\Vert X_i-T(X_1^n)\Vert }, \) 
